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HW7 - described by force free Euler equations Ignore all...

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Physics 110, Problem set #7 Due on June 1 st , 2010 1. Lagrange plank (30 pts): Follow the derivation in 11.11 of Thornton, solve the “asymmetric plank with one point fixed under gravity” problem, as shown. Discuss the conservation laws. You should be able to reduce this problem to a single differential equation. The dimension of the plank = l × l/ 2, mass = M . 2. Hula hoop (20 pts). a. Show that the rotation of a rigid body thrown in midair (under gravity) is
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Unformatted text preview: described by force free Euler equations. Ignore all friction. (5 pts) b. A force-free ring (radius r and mass M ) is spinning around it axis of symmetry with angular frequency ω . What is the frequency of a small wobbling motion (in the fixed frame)? Use the results from section 11.10 of Thornton. (15 pts) 3. Hamiltonian (30 pts): Find the Hamiltonian and the canonical equations for Problems (1)(2)(3) of HW#3 (downloadable from the coursework website)....
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